[en] Due to the emergence of non-terrestrial platformswith extensive coverage, flexible deployment, and reconfigurablecharacteristics, the hybrid satellite-aerial-terrestrial networks(HSATNs) can accommodate a great variety of wireless accessservices in different applications. To effectively reduce the trans-mission latency and facilitate the frequent update of files withimproved spectrum efficiency, we investigate the performanceof cache-enabled HSATN, where the user retrieves the requiredcontent files from the cache-enabled aerial relay or the satellitewith the non-orthogonal multiple access (NOMA) scheme. If therequired content files of the user are cached in the aerial relay,the cache-enabled relay would serve directly. Otherwise, the userwould retrieve the content file from the satellite system, where thesatellite system seeks opportunities for proactive content pushingto the relay during the user content delivery phase. Specifically,taking into account the uncertainty of the number and locationof aerial relays, along with the channel fading of terrestrialusers, the outage probability and hit probability of the considerednetwork are, respectively, derived based on stochastic geometry.Numerical results unveil the effectiveness of the cache-enabledHSATN with the NOMA scheme and proclaim the influence ofkey factors on the system performance. The realistic, tractable,and expandable framework, as well as associated methodology,provide both useful guidance and a solid foundation for evolvednetworks with advanced configurations in the performance ofcache-enabled HSATN.